Part 1) Write pseudocode for an iterative algorithm which finds the maximum value of a list of integers. Use a loop invariant to prove your algorithm is correct. (Presumably you have already witten a program like this over the course of your studies! The interesting part here is the proof.) Part 2) Prove by induction the recursive program Foo is correct: Foo determines if there are two indices i and j, p

Part 1) Write pseudocode for an iterative algorithm which finds the maximum value of a list of integers. Use a loop invariant to prove your algorithm is correct. (Presumably you have already witten a program like this over the course of your studies! The interesting part here is the proof.) Part 2) Prove by induction the recursive program Foo is correct: Foo determines if there are two indices i and j, p

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter15: Recursion

Section: Chapter Questions

Problem 17PE

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Q4. Recursion Find how many possible combinations that a number can be decomposed into the multiple of integers (smaller than the number itself) by a recursion function.Suppose we have a positive number Y as input, and it need to be decomposed into the multiple of several integers, Yi, where each Yi, is smaller than Y(e.g., Y=Y1∗Y2∗ Y3∗...∗Yn). In addition, these decomposed integers can only be arranged in an ascending order (Y1
Artificial Intelligence (Part - 2) ==================== The Towers of Hanoi is a famous problem for studying recursion incomputer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (2) What is the size of the state space?
Recursion can be direct or indirect. It is direct when a function calls itself and it is indirect recursion when a function calls another function that then calls the first function. To illustrate solving a problem using recursion, consider the Fibonacci series: - 1,1,2,3,5,8,13,21,34...The way to solve this problem is to examine the series carefully. The first two numbers are 1. Each subsequent number is the sum of the previous two numbers. Thus, the seventh number is the sum of the sixth and fifth numbers. More generally, the nth number is the sum of n - 2 and n - 1, as long as n > 2.Recursive functions need a stop condition. Something must happen to cause the program to stop recursing, or it will never end. In the Fibonacci series, n < 3 is a stop condition. The algorithm to use is this: 1. Ask the user for a position in the series.2. Call the fib () function with that position, passing in the value the user entered.3. The fib () function examines the argument (n). If n < 3…
Artificial Intelligence (Part - 1) ==================== The Towers of Hanoi is a famous problem for studying recursion in computer science and searching in artificial intelligence. We start with N discs of varying sizes on a peg (stacked in order according to size), and two empty pegs. We are allowed to move a disc from one peg to another, but we are never allowed to move a larger disc on top of a smaller disc. The goal is to move all the discs to the rightmost peg (see figure). To solve the problem by using search methods, we need first formulate the problem. Supposing there are K pegs and N disk. (1) Propose a state representation for the problem?
Write a recursive function to implement the recursive algorithm (multiplying two positive integers using repeated addition). Also, write a program to test your function.
The Tower of Hanoi is a puzzle where n disks of different sizes arestacked in ascending order on one rod and there are two other rods with nodisks on them. The objective is to move all disks from the first rod to thethird, such that:- only one disk is moved at a time- a larger disk can never be placed on top of a smaller oneWrite a recursive function that outputs the sequence of steps needed tosolve the puzzle with n disks.Write a test program in C++ that allows the user to input number of disks andthen uses your function to output the steps needed to solve the puzzle.Hint: If you could move up n−1 of the disks from the first post to thethird post using the second post as a spare, the last disk could be moved fromthe first post to the second post. Then by using the same technique you canmove the n−1 disks from the third post to the second post, using the firstdisk as a spare. There! You have the puzzle solved. You only have to decidewhat the nonrecursive case is, what the recursive…
Computer Science A) If the values of c and d are given and the function Euclid(c,d) below is executed, multiple recursive calls (Bolded at function) are performed to obtain gcd(c,d) and terminate. Give examples of c and d that make exactly 7 recursive calls, and show the process. However, c>d>=1. Euclid(c,d) if d=0 then return c else return Euclid(d,c mod d)
Iteration versus one-friend recursion. 1. Your job is to accept the tuple a1, a2,..., a and return the tuple an, an1,..., a1 that has been reversed. You will only take an element off of one end or put an element back on one end because you are being indolent. But you have allies in recursion who can assist you.Please include the recursive code as well as a paragraph with the friend's description of the algorithm. 2. Now imagine that you lack pals but have a stack. (Refer to Chapter 3. Quickly design an incremental programme to address this issue. Include loop invariants and other crucial stages that are necessary to describe an iterative algorithm. 3. Trace both of these scripts separately. Compare and contrast their computerised calculations step by step.
Using Python Recursion is the concept of a function calling itself until the problem is solved when the Base Case is met. Study Recursion: See slides in Modules, Practice Slides, lab12 and also Recursion is in chapter 9 of the textbook. Some examples of recursion are: compute [ factorial of a number, towers of Hanoi, fractals (as shown in the textbook), and many more]. Example: See slides Page 2 For this assignment we'll use Collatz Cojecture (see Wikipedia). Collatz Conjecture algorithm: Given a number n, first call to the function: f(n): In the function: if n == 1 return 1: if n is even then f(n/2), i.e. call self with the new value. else (n is odd) call self with the new value, f((n*3)+1) and repeat. All numbers eventually end up with 1. The program should test for the base case which is: if n == 1, in which case it returns to the caller with 1. This problem is perfect to demonstrate Recursion.Create a list with random numbers (you can just do this part manually) in the list as 1,…
T/F 7. The recursive procedure for solving the Towers of Hanoi can only be used if the number of discs parameter is 7 or less.
Give the sequence of values of p and q that are computed when Euclid’s algorithm is used to compute the greatest common divisor of 105 and 24. Extend the codegiven on page 4 to develop a program Euclid that takes two integers from the commandline and computes their greatest common divisor, printing out the two arguments foreach call on the recursive method. Use your program to compute the greatest commondivisor or 1111111 and 1234567.
Remove the left recursion from the productions: S ->A a |b A ->A c |S d | €